Answer
The new rate of rotation is $1.49~rev/s$
Work Step by Step
We can use conservation of angular momentum to find the final angular speed:
$L_f = L_0$
$I_f~\omega_f = I_0~\omega_0$
$\omega_f = \frac{I_0~\omega_0}{I_f}$
$\omega_f = \frac{I_0~\omega_0}{0.67~I_0}$
$\omega_f = \frac{1.0~rev/s}{0.67}$
$\omega_f = 1.49~rad/s$
The new rate of rotation is $1.49~rev/s$.
